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Twelve-tone technique

The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer,[not verified in body] who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note[3] through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. Over time, the technique increased greatly in popularity and eventually became widely influential on 20th-century composers. Many important composers who had originally not subscribed to or actively opposed the technique, such as Aaron Copland and Igor Stravinsky,[clarification needed] eventually adopted it in their music.

Arnold Schoenberg, inventor of twelve-tone technique

Schoenberg himself described the system as a "Method of composing with twelve tones which are related only with one another".[4] It is commonly considered a form of serialism.

Schoenberg's fellow countryman and contemporary Hauer also developed a similar system using unordered hexachords or tropes—but with no connection to Schoenberg's twelve-tone technique.[contradictory] Other composers have created systematic use of the chromatic scale, but Schoenberg's method is considered to be most historically and aesthetically significant.[5]

History of use edit

Though most sources will say it was invented by Austrian composer Arnold Schoenberg in 1921 and first described privately to his associates in 1923, in fact Josef Matthias Hauer published his "law of the twelve tones" in 1919, requiring that all twelve chromatic notes sound before any note is repeated.[8][failed verification] The method was used during the next twenty years almost exclusively by the composers of the Second Viennese SchoolAlban Berg, Anton Webern, and Schoenberg himself.

The twelve tone technique was preceded by "freely" atonal pieces of 1908–1923 which, though "free", often have as an "integrative element ... a minute intervallic cell" which in addition to expansion may be transformed as with a tone row, and in which individual notes may "function as pivotal elements, to permit overlapping statements of a basic cell or the linking of two or more basic cells".[9] The twelve-tone technique was also preceded by "nondodecaphonic serial composition" used independently in the works of Alexander Scriabin, Igor Stravinsky, Béla Bartók, Carl Ruggles, and others.[10] Oliver Neighbour argues that Bartók was "the first composer to use a group of twelve notes consciously for a structural purpose", in 1908 with the third of his fourteen bagatelles.[11] "Essentially, Schoenberg and Hauer systematized and defined for their own dodecaphonic purposes a pervasive technical feature of 'modern' musical practice, the ostinato".[10] Additionally, John Covach argues that the strict distinction between the two, emphasized by authors including Perle, is overemphasized:

The distinction often made between Hauer and the Schoenberg school—that the former's music is based on unordered hexachords while the latter's is based on an ordered series—is false: while he did write pieces that could be thought of as "trope pieces", much of Hauer's twelve-tone music employs an ordered series.[12]

The "strict ordering" of the Second Viennese school, on the other hand, "was inevitably tempered by practical considerations: they worked on the basis of an interaction between ordered and unordered pitch collections."[13]

Rudolph Reti, an early proponent, says: "To replace one structural force (tonality) by another (increased thematic oneness) is indeed the fundamental idea behind the twelve-tone technique", arguing it arose out of Schoenberg's frustrations with free atonality,[14][page needed] providing a "positive premise" for atonality.[3] In Hauer's breakthrough piece Nomos, Op. 19 (1919) he used twelve-tone sections to mark out large formal divisions, such as with the opening five statements of the same twelve-tone series, stated in groups of five notes making twelve five-note phrases.[13]

Schoenberg's idea in developing the technique was for it to "replace those structural differentiations provided formerly by tonal harmonies".[4] As such, twelve-tone music is usually atonal, and treats each of the 12 semitones of the chromatic scale with equal importance, as opposed to earlier classical music which had treated some notes as more important than others (particularly the tonic and the dominant note).

The technique became widely used by the fifties, taken up by composers such as Milton Babbitt, Luciano Berio, Pierre Boulez, Luigi Dallapiccola, Ernst Krenek, Riccardo Malipiero, and, after Schoenberg's death, Igor Stravinsky. Some of these composers extended the technique to control aspects other than the pitches of notes (such as duration, method of attack and so on), thus producing serial music. Some even subjected all elements of music to the serial process.

Charles Wuorinen said in a 1962 interview that while "most of the Europeans say that they have 'gone beyond' and 'exhausted' the twelve-tone system", in America, "the twelve-tone system has been carefully studied and generalized into an edifice more impressive than any hitherto known."[15]

American composer Scott Bradley, best known for his musical scores for work like Tom & Jerry and Droopy Dog, utilized the 12-tone technique in his work. Bradley described his use thus:

The Twelve-Tone System provides the 'out-of-this-world' progressions so necessary to under-write the fantastic and incredible situations which present-day cartoons contain.[16]

An example of Bradley's use of the technique to convey building tension occurs in the Tom & Jerry short "Puttin' on the Dog", from 1944. In a scene where the mouse, wearing a dog mask, runs across a yard of dogs "in disguise", a chromatic scale represents both the mouse's movements, and the approach of a suspicious dog, mirrored octaves lower.[17] Apart from his work in cartoon scores, Bradley also composed tone poems that were performed in concert in California.[18]

Rock guitarist Ron Jarzombek used a twelve-tone system for composing Blotted Science's extended play The Animation of Entomology. He put the notes into a clock and rearranged them to be used that are side by side or consecutive He called his method "Twelve-Tone in Fragmented Rows."[19]

Tone row edit

The basis of the twelve-tone technique is the tone row, an ordered arrangement of the twelve notes of the chromatic scale (the twelve equal tempered pitch classes). There are four postulates or preconditions to the technique which apply to the row (also called a set or series), on which a work or section is based:[20]

  1. The row is a specific ordering of all twelve notes of the chromatic scale (without regard to octave placement).
  2. No note is repeated within the row.
  3. The row may be subjected to interval-preserving transformations—that is, it may appear in inversion (denoted I), retrograde (R), or retrograde-inversion (RI), in addition to its "original" or prime form (P).
  4. The row in any of its four transformations may begin on any degree of the chromatic scale; in other words it may be freely transposed. (Transposition being an interval-preserving transformation, this is technically covered already by 3.) Transpositions are indicated by an integer between 0 and 11 denoting the number of semitones: thus, if the original form of the row is denoted P0, then P1 denotes its transposition upward by one semitone (similarly I1 is an upward transposition of the inverted form, R1 of the retrograde form, and RI1 of the retrograde-inverted form).

(In Hauer's system postulate 3 does not apply.)[2]

A particular transformation (prime, inversion, retrograde, retrograde-inversion) together with a choice of transpositional level is referred to as a set form or row form. Every row thus has up to 48 different row forms. (Some rows have fewer due to symmetry; see the sections on derived rows and invariance below.)

Example edit

Suppose the prime form of the row is as follows:

 

Then the retrograde is the prime form in reverse order:

 

The inversion is the prime form with the intervals inverted (so that a rising minor third becomes a falling minor third, or equivalently, a rising major sixth):

 

And the retrograde inversion is the inverted row in retrograde:

 

P, R, I and RI can each be started on any of the twelve notes of the chromatic scale, meaning that 47 permutations of the initial tone row can be used, giving a maximum of 48 possible tone rows. However, not all prime series will yield so many variations because transposed transformations may be identical to each other. This is known as invariance. A simple case is the ascending chromatic scale, the retrograde inversion of which is identical to the prime form, and the retrograde of which is identical to the inversion (thus, only 24 forms of this tone row are available).

 
Prime, retrograde, inverted, and retrograde-inverted forms of the ascending chromatic scale. P and RI are the same (to within transposition), as are R and I.

In the above example, as is typical, the retrograde inversion contains three points where the sequence of two pitches are identical to the prime row. Thus the generative power of even the most basic transformations is both unpredictable and inevitable. Motivic development can be driven by such internal consistency.

Application in composition edit

Note that rules 1–4 above apply to the construction of the row itself, and not to the interpretation of the row in the composition. (Thus, for example, postulate 2 does not mean, contrary to common belief, that no note in a twelve-tone work can be repeated until all twelve have been sounded.) While a row may be expressed literally on the surface as thematic material, it need not be, and may instead govern the pitch structure of the work in more abstract ways. Even when the technique is applied in the most literal manner, with a piece consisting of a sequence of statements of row forms, these statements may appear consecutively, simultaneously, or may overlap, giving rise to harmony.

 
Schoenberg's annotated opening of his Wind Quintet Op. 26 shows the distribution of the pitches of the row among the voices and the balance between the hexachords, 1–6 and 7–12, in the principal voice and accompaniment[21]

Durations, dynamics and other aspects of music other than the pitch can be freely chosen by the composer, and there are also no general rules about which tone rows should be used at which time (beyond their all being derived from the prime series, as already explained). However, individual composers have constructed more detailed systems in which matters such as these are also governed by systematic rules (see serialism).

Topography edit

Analyst Kathryn Bailey has used the term 'topography' to describe the particular way in which the notes of a row are disposed in her work on the dodecaphonic music of Webern. She identifies two types of topography in Webern's music: block topography and linear topography.

The former, which she views as the 'simplest', is defined as follows: 'rows are set one after the other, with all notes sounding in the order prescribed by this succession of rows, regardless of texture'. The latter is more complex: the musical texture 'is the product of several rows progressing simultaneously in as many voices' (note that these 'voices' are not necessarily restricted to individual instruments and therefore cut across the musical texture, operating as more of a background structure).[22]

Elisions, Chains, and Cycles edit

Serial rows can be connected through elision, a term that describes 'the overlapping of two rows that occur in succession, so that one or more notes at the juncture are shared (are played only once to serve both rows)'.[23] When this elision incorporates two or more notes it creates a row chain;[24] when multiple rows are connected by the same elision (typically identified as the same in set-class terms) this creates a row chain cycle, which therefore provides a technique for organising groups of rows.[25]

Properties of transformations edit

The tone row chosen as the basis of the piece is called the prime series (P). Untransposed, it is notated as P0. Given the twelve pitch classes of the chromatic scale, there are 12 factorial[26] (479,001,600[13]) tone rows, although this is far higher than the number of unique tone rows (after taking transformations into account). There are 9,985,920 classes of twelve-tone rows up to equivalence (where two rows are equivalent if one is a transformation of the other).[27]

Appearances of P can be transformed from the original in three basic ways:

  • transposition up or down, giving Pχ.
  • reversing the order of the pitches, giving the retrograde (R)
  • turning each interval direction to its opposite, giving the inversion (I).

The various transformations can be combined. These give rise to a set-complex of forty-eight forms of the set, 12 transpositions of the four basic forms: P, R, I, RI. The combination of the retrograde and inversion transformations is known as the retrograde inversion (RI).

RI is: RI of P, R of I, and I of R.
R is: R of P, RI of I, and I of RI.
I is: I of P, RI of R, and R of RI.
P is: R of R, I of I, and RI of RI.

thus, each cell in the following table lists the result of the transformations, a four-group, in its row and column headers:

P: RI: R: I:
RI: P I R
R: I P RI
I: R RI P

However, there are only a few numbers by which one may multiply a row and still end up with twelve tones. (Multiplication is in any case not interval-preserving.)

Derivation edit

Derivation is transforming segments of the full chromatic, fewer than 12 pitch classes, to yield a complete set, most commonly using trichords, tetrachords, and hexachords. A derived set can be generated by choosing appropriate transformations of any trichord except 0,3,6, the diminished triad[citation needed]. A derived set can also be generated from any tetrachord that excludes the interval class 4, a major third, between any two elements. The opposite, partitioning, uses methods to create segments from sets, most often through registral difference.

Combinatoriality edit

Combinatoriality is a side-effect of derived rows where combining different segments or sets such that the pitch class content of the result fulfills certain criteria, usually the combination of hexachords which complete the full chromatic.

Invariance edit

Invariant formations are also the side effect of derived rows where a segment of a set remains similar or the same under transformation. These may be used as "pivots" between set forms, sometimes used by Anton Webern and Arnold Schoenberg.[29]

Invariance is defined as the "properties of a set that are preserved under [any given] operation, as well as those relationships between a set and the so-operationally transformed set that inhere in the operation",[30] a definition very close to that of mathematical invariance. George Perle describes their use as "pivots" or non-tonal ways of emphasizing certain pitches. Invariant rows are also combinatorial and derived.

Cross partition edit

 
Aggregates spanning several local set forms in Schoenberg's Von heute auf morgen.[31]

A cross partition is an often monophonic or homophonic technique which, "arranges the pitch classes of an aggregate (or a row) into a rectangular design", in which the vertical columns (harmonies) of the rectangle are derived from the adjacent segments of the row and the horizontal columns (melodies) are not (and thus may contain non-adjacencies).[32]

For example, the layout of all possible 'even' cross partitions is as follows:[33]

62 43 34 26
** *** **** ******
** *** **** ******
** *** ****
** ***
**
**

One possible realization out of many for the order numbers of the 34 cross partition, and one variation of that, are:[33]

0 3 6 9 0 5 6 e 1 4 7 t 2 3 7 t 2 5 8 e 1 4 8 9 

Thus if one's tone row was 0 e 7 4 2 9 3 8 t 1 5 6, one's cross partitions from above would be:

0 4 3 1 0 9 3 6 e 2 8 5 7 4 8 5 7 9 t 6 e 2 t 1 

Cross partitions are used in Schoenberg's Op. 33a Klavierstück and also by Berg but Dallapicolla used them more than any other composer.[34]

Other edit

In practice, the "rules" of twelve-tone technique have been bent and broken many times, not least by Schoenberg himself. For instance, in some pieces two or more tone rows may be heard progressing at once, or there may be parts of a composition which are written freely, without recourse to the twelve-tone technique at all. Offshoots or variations may produce music in which:

  • the full chromatic is used and constantly circulates, but permutational devices are ignored
  • permutational devices are used but not on the full chromatic

Also, some composers, including Stravinsky, have used cyclic permutation, or rotation, where the row is taken in order but using a different starting note. Stravinsky also preferred the inverse-retrograde, rather than the retrograde-inverse, treating the former as the compositionally predominant, "untransposed" form.[35]

Although usually atonal, twelve tone music need not be—several pieces by Berg, for instance, have tonal elements.

One of the best known twelve-note compositions is Variations for Orchestra by Arnold Schoenberg. "Quiet", in Leonard Bernstein's Candide, satirizes the method by using it for a song about boredom, and Benjamin Britten used a twelve-tone row—a "tema seriale con fuga"—in his Cantata Academica: Carmen Basiliense (1959) as an emblem of academicism.[36]

Schoenberg's mature practice edit

Ten features of Schoenberg's mature twelve-tone practice are characteristic, interdependent, and interactive:[37]

  1. Hexachordal inversional combinatoriality
  2. Aggregates
  3. Linear set presentation
  4. Partitioning
  5. Isomorphic partitioning
  6. Invariants
  7. Hexachordal levels
  8. Harmony, "consistent with and derived from the properties of the referential set"
  9. Metre, established through "pitch-relational characteristics"
  10. Multidimensional set presentations.

See also edit

References edit

Notes edit

  1. ^ Whittall 2008, 26.
  2. ^ a b Perle 1991, 145.
  3. ^ a b Perle 1977, 2.
  4. ^ a b Schoenberg 1975, 218.
  5. ^ Whittall 2008, 25.
  6. ^ Leeuw 2005, 149.
  7. ^ Leeuw 2005, 155–157.
  8. ^ Schoenberg 1975, 213.
  9. ^ Perle 1977, 9–10.
  10. ^ a b Perle 1977, 37.
  11. ^ Neighbour 1955, 53.
  12. ^ John Covach quoted in Whittall 2008, 24.
  13. ^ a b c Whittall 2008, 24.
  14. ^ Reti 1958
  15. ^ Chase 1987, 587.
  16. ^ Yowp (7 January 2017). "Tralfaz: Cartoon Composer Scott Bradley".
  17. ^ Goldmark, Daniel (2007). Tunes for 'Toons: Music and the Hollywood Cartoon. Univ of California Press. p. 71. ISBN 978-0-520-25311-7.
  18. ^ Scott Bradley at IMDb
  19. ^ Mustein, Dave (2 November 2011). "Blotted Science's Ron Jarzombek: The Twelve-tone Metalsucks Interview". MetalSucks. Retrieved 19 January 2021.
  20. ^ Perle 1977, 3.
  21. ^ Whittall 2008, 52.
  22. ^ Bailey, Kathryn (2006). The twelve-note music of Anton Webern: old forms in a new language. Music in the twentieth century (Digitally printed 1st pbk. version ed.). Cambridge [England] New York: Cambridge University Press. p. 31. ISBN 978-0-521-39088-0.
  23. ^ Bailey, Kathryn (2006). The twelve-note music of Anton Webern: old forms in a new language. Music in the twentieth century (Digitally printed 1st pbk. version ed.). Cambridge [England] New York: Cambridge University Press. p. 449. ISBN 978-0-521-39088-0.
  24. ^ Moseley, Brian (1 September 2019). "Transformation Chains, Associative Areas, and a Principle of Form for Anton Webern's Twelve-tone Music". Music Theory Spectrum. 41 (2): 218–243. doi:10.1093/mts/mtz010. ISSN 0195-6167.
  25. ^ Moseley, Brian (2018). "Cycles in Webern's Late Music". Journal of Music Theory. 62 (2): 165–204. doi:10.1215/00222909-7127658. ISSN 0022-2909. S2CID 171497028.
  26. ^ Loy 2007, 310.
  27. ^ Benson 2007, 348.
  28. ^ Haimo 1990, 27.
  29. ^ Perle 1977, 91–93.
  30. ^ Babbitt 1960, 249–250.
  31. ^ Haimo 1990, 13.
  32. ^ Alegant 2010, 20.
  33. ^ a b Alegant 2010, 21.
  34. ^ Alegant 2010, 22, 24.
  35. ^ Spies 1965, 118.
  36. ^ Brett 2007.
  37. ^ Haimo 1990, 41.

Sources edit

  • Alegant, Brian. 2010. The Twelve-Tone Music of Luigi Dallapiccola. Eastman Studies in Music 76. Rochester, New York: University of Rochester Press. ISBN 978-1-58046-325-6.
  • Babbitt, Milton. 1960. "Twelve-Tone Invariants as Compositional Determinants". The Musical Quarterly 46, no. 2, Special Issue: Problems of Modern Music: The Princeton Seminar in Advanced Musical Studies (April): 246–259. doi:10.1093/mq/XLVI.2.246. JSTOR 740374(subscription required).
  • Babbitt, Milton. 1961. "Set Structure as a Compositional Determinant". Journal of Music Theory 5, no. 1 (Spring): 72–94. JSTOR 842871(subscription required).
  • Benson, Dave. 2007 Music: A Mathematical Offering. Cambridge and New York: Cambridge University Press. ISBN 978-0-521-85387-3.
  • Brett, Philip. "Britten, Benjamin." Grove Music Online ed. L. Macy (Accessed 8 January 2007)
  • Chase, Gilbert. 1987. America's Music: From the Pilgrims to the Present, revised third edition. Music in American Life. Urbana: University of Illinois Press. ISBN 0-252-00454-X (cloth); ISBN 0-252-06275-2 (pbk).
  • Haimo, Ethan. 1990. Schoenberg's Serial Odyssey: The Evolution of his Twelve-Tone Method, 1914–1928. Oxford [England] Clarendon Press; New York: Oxford University Press ISBN 0-19-315260-6.
  • Hill, Richard S. 1936. "Schoenberg's Tone-Rows and the Tonal System of the Future". The Musical Quarterly 22, no. 1 (January): 14–37. doi:10.1093/mq/XXII.1.14. JSTOR 739013(subscription required).
  • Lansky, Paul; George Perle and Dave Headlam. 2001. "Twelve-note Composition". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
  • Leeuw, Ton de. 2005. Music of the Twentieth Century: A Study of Its Elements and Structure, translated from the Dutch by Stephen Taylor. Amsterdam: Amsterdam University Press. ISBN 90-5356-765-8. Translation of Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur. Utrecht: Oosthoek, 1964. Third impression, Utrecht: Bohn, Scheltema & Holkema, 1977. ISBN 90-313-0244-9.
  • Loy, D. Gareth, 2007. Musimathics: The Mathematical Foundations of Music, Vol. 1. Cambridge, Massachusetts and London: MIT Press. ISBN 978-0-262-12282-5.
  • Neighbour, Oliver. 1954. "The Evolution of Twelve-Note Music". Proceedings of the Royal Musical Association, volume 81, issue 1: 49–61. doi:10.1093/jrma/81.1.49
  • Perle, George. 1977. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, fourth edition, revised. Berkeley, Los Angeles, and London: University of California Press. ISBN 0-520-03395-7
  • Perle, George. 1991. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, sixth edition, revised. Berkeley: University of California Press. ISBN 978-0-520-07430-9.
  • Reti, Rudolph. 1958. Tonality, Atonality, Pantonality: A Study of Some Trends in Twentieth Century Music. Westport, Connecticut: Greenwood Press. ISBN 0-313-20478-0.
  • Rufer, Josef. 1954. Composition with Twelve Notes Related Only to One Another, translated by Humphrey Searle. New York: The Macmillan Company. (Original German ed., 1952)
  • Schoenberg, Arnold. 1975. Style and Idea, edited by Leonard Stein with translations by Leo Black. Berkeley & Los Angeles: University of California Press. ISBN 0-520-05294-3.
    • 207–208 "Twelve-Tone Composition (1923)"
    • 214–245 "Composition with Twelve Tones (1) (1941)"
    • 245–249 "Composition with Twelve Tones (2) (c. 1948)"
  • Solomon, Larry. 1973. "New Symmetric Transformations". Perspectives of New Music 11, no. 2 (Spring–Summer): 257–264. JSTOR 832323(subscription required).
  • Spies, Claudio. 1965. "Notes on Stravinsky's Abraham and Isaac". Perspectives of New Music 3, no. 2 (Spring–Summer): 104–126. JSTOR 832508(subscription required).
  • Whittall, Arnold. 2008. The Cambridge Introduction to Serialism. Cambridge Introductions to Music. New York: Cambridge University Press. ISBN 978-0-521-86341-4 (cloth) ISBN 978-0-521-68200-8 (pbk).

Further reading edit

  • Covach, John. 1992. "The Zwölftonspiel of Josef Matthias Hauer". Journal of Music Theory 36, no. 1 (Spring): 149–84. JSTOR 843913(subscription required).
  • Covach, John. 2000. "Schoenberg's 'Poetics of Music', the Twelve-tone Method, and the Musical Idea". In Schoenberg and Words: The Modernist Years, edited by Russell A. Berman and Charlotte M. Cross, New York: Garland. ISBN 0-8153-2830-3
  • Covach, John. 2002, "Twelve-tone Theory". In The Cambridge History of Western Music Theory, edited by Thomas Christensen, 603–627. Cambridge: Cambridge University Press. ISBN 0-521-62371-5.
  • Krenek, Ernst. 1953. "Is the Twelve-Tone Technique on the Decline?" The Musical Quarterly 39, no 4 (October): 513–527.
  • Šedivý, Dominik. 2011. Serial Composition and Tonality. An Introduction to the Music of Hauer and Steinbauer, edited by Günther Friesinger, Helmut Neumann and Dominik Šedivý. Vienna: edition mono. ISBN 3-902796-03-0
  • Sloan, Susan L. 1989. "Archival Exhibit: Schoenberg's Dodecaphonic Devices". Journal of the Arnold Schoenberg Institute 12, no. 2 (November): 202–205.
  • Starr, Daniel. 1978. "Sets, Invariance and Partitions". Journal of Music Theory 22, no. 1 (Spring): 1–42. JSTOR 843626(subscription required).
  • Wuorinen, Charles. 1979. Simple Composition. New York: Longman. ISBN 0-582-28059-1. Reprinted 1991, New York: C. F. Peters. ISBN 0-938856-06-5.

External links edit

  • Twelve tone square to find all combinations of a 12 tone sequence
  • by Larry Solomon
  • Javascript twelve tone matrix calculator and tone row analyzer
  • Matrix generator from musictheory.net by Ricci Adams
  • Twelve-Tone Technique, A Quick Reference by Dan Román
  • Twelve Tones by mathemusician Vi Hart on YouTube
  • Dodecaphonic Knots and Topology of Words by Franck Jedrzejewski [fr]

twelve, tone, technique, confused, with, twelve, tone, equal, temperament, twelve, tone, technique, also, known, dodecaphony, twelve, tone, serialism, british, usage, twelve, note, composition, method, musical, composition, first, devised, austrian, composer, . Not to be confused with twelve tone equal temperament The twelve tone technique also known as dodecaphony twelve tone serialism and in British usage twelve note composition is a method of musical composition first devised by Austrian composer Josef Matthias Hauer not verified in body who published his law of the twelve tones in 1919 In 1923 Arnold Schoenberg 1874 1951 developed his own better known version of 12 tone technique which became associated with the Second Viennese School composers who were the primary users of the technique in the first decades of its existence The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note 3 through the use of tone rows orderings of the 12 pitch classes All 12 notes are thus given more or less equal importance and the music avoids being in a key Over time the technique increased greatly in popularity and eventually became widely influential on 20th century composers Many important composers who had originally not subscribed to or actively opposed the technique such as Aaron Copland and Igor Stravinsky clarification needed eventually adopted it in their music Arnold Schoenberg inventor of twelve tone techniqueJosef Matthias Hauer s athematic dodecaphony in Nomos Op 19 1 source source source Example of Hauer s tropes 2 source source source Problems playing these files See media help Schoenberg himself described the system as a Method of composing with twelve tones which are related only with one another 4 It is commonly considered a form of serialism Schoenberg s fellow countryman and contemporary Hauer also developed a similar system using unordered hexachords or tropes but with no connection to Schoenberg s twelve tone technique contradictory Other composers have created systematic use of the chromatic scale but Schoenberg s method is considered to be most historically and aesthetically significant 5 Contents 1 History of use 2 Tone row 2 1 Example 2 2 Application in composition 2 2 1 Topography 2 2 2 Elisions Chains and Cycles 2 3 Properties of transformations 2 4 Derivation 2 4 1 Combinatoriality 2 4 2 Invariance 2 5 Cross partition 2 6 Other 3 Schoenberg s mature practice 4 See also 5 References 5 1 Notes 5 2 Sources 5 3 Further reading 6 External linksHistory of use edit nbsp Schoenberg s Op 23 mov 5 mm 1 4 source source source The first 12 note work 6 nbsp Schoenberg s Piano Piece Op 33a source source source The principal forms P1 and I6 of Schoenberg s Piano Piece Op 33a tone row feature hexachordal combinatoriality and contains three perfect fifths each which is the relation between P1 and I6 and a source of contrast between accumulations of 5ths and generally more complex simultaneity 7 For example group A consists of B C F B while the more blended group B consists of A C D F nbsp Problems playing these files See media help Though most sources will say it was invented by Austrian composer Arnold Schoenberg in 1921 and first described privately to his associates in 1923 in fact Josef Matthias Hauer published his law of the twelve tones in 1919 requiring that all twelve chromatic notes sound before any note is repeated 8 failed verification The method was used during the next twenty years almost exclusively by the composers of the Second Viennese School Alban Berg Anton Webern and Schoenberg himself The twelve tone technique was preceded by freely atonal pieces of 1908 1923 which though free often have as an integrative element a minute intervallic cell which in addition to expansion may be transformed as with a tone row and in which individual notes may function as pivotal elements to permit overlapping statements of a basic cell or the linking of two or more basic cells 9 The twelve tone technique was also preceded by nondodecaphonic serial composition used independently in the works of Alexander Scriabin Igor Stravinsky Bela Bartok Carl Ruggles and others 10 Oliver Neighbour argues that Bartok was the first composer to use a group of twelve notes consciously for a structural purpose in 1908 with the third of his fourteen bagatelles 11 Essentially Schoenberg and Hauer systematized and defined for their own dodecaphonic purposes a pervasive technical feature of modern musical practice the ostinato 10 Additionally John Covach argues that the strict distinction between the two emphasized by authors including Perle is overemphasized The distinction often made between Hauer and the Schoenberg school that the former s music is based on unordered hexachords while the latter s is based on an ordered series is false while he did write pieces that could be thought of as trope pieces much of Hauer s twelve tone music employs an ordered series 12 The strict ordering of the Second Viennese school on the other hand was inevitably tempered by practical considerations they worked on the basis of an interaction between ordered and unordered pitch collections 13 Rudolph Reti an early proponent says To replace one structural force tonality by another increased thematic oneness is indeed the fundamental idea behind the twelve tone technique arguing it arose out of Schoenberg s frustrations with free atonality 14 page needed providing a positive premise for atonality 3 In Hauer s breakthrough piece Nomos Op 19 1919 he used twelve tone sections to mark out large formal divisions such as with the opening five statements of the same twelve tone series stated in groups of five notes making twelve five note phrases 13 Schoenberg s idea in developing the technique was for it to replace those structural differentiations provided formerly by tonal harmonies 4 As such twelve tone music is usually atonal and treats each of the 12 semitones of the chromatic scale with equal importance as opposed to earlier classical music which had treated some notes as more important than others particularly the tonic and the dominant note The technique became widely used by the fifties taken up by composers such as Milton Babbitt Luciano Berio Pierre Boulez Luigi Dallapiccola Ernst Krenek Riccardo Malipiero and after Schoenberg s death Igor Stravinsky Some of these composers extended the technique to control aspects other than the pitches of notes such as duration method of attack and so on thus producing serial music Some even subjected all elements of music to the serial process Charles Wuorinen said in a 1962 interview that while most of the Europeans say that they have gone beyond and exhausted the twelve tone system in America the twelve tone system has been carefully studied and generalized into an edifice more impressive than any hitherto known 15 American composer Scott Bradley best known for his musical scores for work like Tom amp Jerry and Droopy Dog utilized the 12 tone technique in his work Bradley described his use thus The Twelve Tone System provides the out of this world progressions so necessary to under write the fantastic and incredible situations which present day cartoons contain 16 An example of Bradley s use of the technique to convey building tension occurs in the Tom amp Jerry short Puttin on the Dog from 1944 In a scene where the mouse wearing a dog mask runs across a yard of dogs in disguise a chromatic scale represents both the mouse s movements and the approach of a suspicious dog mirrored octaves lower 17 Apart from his work in cartoon scores Bradley also composed tone poems that were performed in concert in California 18 Rock guitarist Ron Jarzombek used a twelve tone system for composing Blotted Science s extended play The Animation of Entomology He put the notes into a clock and rearranged them to be used that are side by side or consecutive He called his method Twelve Tone in Fragmented Rows 19 Tone row editMain article Tone row nbsp Sehr langsam source source Sample of Sehr langsam from String Trio Op 20 by Anton Webern an example of the twelve tone technique a type of serialism Problems playing this file See media help The basis of the twelve tone technique is the tone row an ordered arrangement of the twelve notes of the chromatic scale the twelve equal tempered pitch classes There are four postulates or preconditions to the technique which apply to the row also called a set or series on which a work or section is based 20 The row is a specific ordering of all twelve notes of the chromatic scale without regard to octave placement No note is repeated within the row The row may be subjected to interval preserving transformations that is it may appear in inversion denoted I retrograde R or retrograde inversion RI in addition to its original or prime form P The row in any of its four transformations may begin on any degree of the chromatic scale in other words it may be freely transposed Transposition being an interval preserving transformation this is technically covered already by 3 Transpositions are indicated by an integer between 0 and 11 denoting the number of semitones thus if the original form of the row is denoted P0 then P1 denotes its transposition upward by one semitone similarly I1 is an upward transposition of the inverted form R1 of the retrograde form and RI1 of the retrograde inverted form In Hauer s system postulate 3 does not apply 2 A particular transformation prime inversion retrograde retrograde inversion together with a choice of transpositional level is referred to as a set form or row form Every row thus has up to 48 different row forms Some rows have fewer due to symmetry see the sections on derived rows and invariance below Example edit Suppose the prime form of the row is as follows nbsp Then the retrograde is the prime form in reverse order nbsp The inversion is the prime form with the intervals inverted so that a rising minor third becomes a falling minor third or equivalently a rising major sixth nbsp And the retrograde inversion is the inverted row in retrograde nbsp P R I and RI can each be started on any of the twelve notes of the chromatic scale meaning that 47 permutations of the initial tone row can be used giving a maximum of 48 possible tone rows However not all prime series will yield so many variations because transposed transformations may be identical to each other This is known as invariance A simple case is the ascending chromatic scale the retrograde inversion of which is identical to the prime form and the retrograde of which is identical to the inversion thus only 24 forms of this tone row are available nbsp Prime retrograde inverted and retrograde inverted forms of the ascending chromatic scale P and RI are the same to within transposition as are R and I In the above example as is typical the retrograde inversion contains three points where the sequence of two pitches are identical to the prime row Thus the generative power of even the most basic transformations is both unpredictable and inevitable Motivic development can be driven by such internal consistency Application in composition edit Note that rules 1 4 above apply to the construction of the row itself and not to the interpretation of the row in the composition Thus for example postulate 2 does not mean contrary to common belief that no note in a twelve tone work can be repeated until all twelve have been sounded While a row may be expressed literally on the surface as thematic material it need not be and may instead govern the pitch structure of the work in more abstract ways Even when the technique is applied in the most literal manner with a piece consisting of a sequence of statements of row forms these statements may appear consecutively simultaneously or may overlap giving rise to harmony nbsp Schoenberg s annotated opening of his Wind Quintet Op 26 shows the distribution of the pitches of the row among the voices and the balance between the hexachords 1 6 and 7 12 in the principal voice and accompaniment 21 Durations dynamics and other aspects of music other than the pitch can be freely chosen by the composer and there are also no general rules about which tone rows should be used at which time beyond their all being derived from the prime series as already explained However individual composers have constructed more detailed systems in which matters such as these are also governed by systematic rules see serialism Topography edit Analyst Kathryn Bailey has used the term topography to describe the particular way in which the notes of a row are disposed in her work on the dodecaphonic music of Webern She identifies two types of topography in Webern s music block topography and linear topography The former which she views as the simplest is defined as follows rows are set one after the other with all notes sounding in the order prescribed by this succession of rows regardless of texture The latter is more complex the musical texture is the product of several rows progressing simultaneously in as many voices note that these voices are not necessarily restricted to individual instruments and therefore cut across the musical texture operating as more of a background structure 22 Elisions Chains and Cycles edit Serial rows can be connected through elision a term that describes the overlapping of two rows that occur in succession so that one or more notes at the juncture are shared are played only once to serve both rows 23 When this elision incorporates two or more notes it creates a row chain 24 when multiple rows are connected by the same elision typically identified as the same in set class terms this creates a row chain cycle which therefore provides a technique for organising groups of rows 25 Properties of transformations edit The tone row chosen as the basis of the piece is called the prime series P Untransposed it is notated as P0 Given the twelve pitch classes of the chromatic scale there are 12 factorial 26 479 001 600 13 tone rows although this is far higher than the number of unique tone rows after taking transformations into account There are 9 985 920 classes of twelve tone rows up to equivalence where two rows are equivalent if one is a transformation of the other 27 Appearances of P can be transformed from the original in three basic ways transposition up or down giving Px reversing the order of the pitches giving the retrograde R turning each interval direction to its opposite giving the inversion I The various transformations can be combined These give rise to a set complex of forty eight forms of the set 12 transpositions of the four basic forms P R I RI The combination of the retrograde and inversion transformations is known as the retrograde inversion RI RI is RI of P R of I and I of R R is R of P RI of I and I of RI I is I of P RI of R and R of RI P is R of R I of I and RI of RI thus each cell in the following table lists the result of the transformations a four group in its row and column headers P RI R I RI P I RR I P RII R RI PHowever there are only a few numbers by which one may multiply a row and still end up with twelve tones Multiplication is in any case not interval preserving Derivation edit Main article Derived row Derivation is transforming segments of the full chromatic fewer than 12 pitch classes to yield a complete set most commonly using trichords tetrachords and hexachords A derived set can be generated by choosing appropriate transformations of any trichord except 0 3 6 the diminished triad citation needed A derived set can also be generated from any tetrachord that excludes the interval class 4 a major third between any two elements The opposite partitioning uses methods to create segments from sets most often through registral difference Combinatoriality edit Main article Combinatoriality Combinatoriality is a side effect of derived rows where combining different segments or sets such that the pitch class content of the result fulfills certain criteria usually the combination of hexachords which complete the full chromatic Invariance edit nbsp Schoenberg s Concerto for Violin source source source nbsp Hexachord invariance 28 The last hexachord of P0 C C G A D F contains the same pitches as the first hexachord of I5 D C A C G F Problems playing this file See media help Invariant formations are also the side effect of derived rows where a segment of a set remains similar or the same under transformation These may be used as pivots between set forms sometimes used by Anton Webern and Arnold Schoenberg 29 Invariance is defined as the properties of a set that are preserved under any given operation as well as those relationships between a set and the so operationally transformed set that inhere in the operation 30 a definition very close to that of mathematical invariance George Perle describes their use as pivots or non tonal ways of emphasizing certain pitches Invariant rows are also combinatorial and derived Cross partition edit nbsp Aggregates spanning several local set forms in Schoenberg s Von heute auf morgen 31 See also Derived row Partition and mosaic A cross partition is an often monophonic or homophonic technique which arranges the pitch classes of an aggregate or a row into a rectangular design in which the vertical columns harmonies of the rectangle are derived from the adjacent segments of the row and the horizontal columns melodies are not and thus may contain non adjacencies 32 For example the layout of all possible even cross partitions is as follows 33 62 43 34 26 One possible realization out of many for the order numbers of the 34 cross partition and one variation of that are 33 0 3 6 9 0 5 6 e 1 4 7 t 2 3 7 t 2 5 8 e 1 4 8 9 Thus if one s tone row was 0 e 7 4 2 9 3 8 t 1 5 6 one s cross partitions from above would be 0 4 3 1 0 9 3 6 e 2 8 5 7 4 8 5 7 9 t 6 e 2 t 1 Cross partitions are used in Schoenberg s Op 33a Klavierstuck and also by Berg but Dallapicolla used them more than any other composer 34 Other edit In practice the rules of twelve tone technique have been bent and broken many times not least by Schoenberg himself For instance in some pieces two or more tone rows may be heard progressing at once or there may be parts of a composition which are written freely without recourse to the twelve tone technique at all Offshoots or variations may produce music in which the full chromatic is used and constantly circulates but permutational devices are ignored permutational devices are used but not on the full chromaticAlso some composers including Stravinsky have used cyclic permutation or rotation where the row is taken in order but using a different starting note Stravinsky also preferred the inverse retrograde rather than the retrograde inverse treating the former as the compositionally predominant untransposed form 35 Although usually atonal twelve tone music need not be several pieces by Berg for instance have tonal elements One of the best known twelve note compositions is Variations for Orchestra by Arnold Schoenberg Quiet in Leonard Bernstein s Candide satirizes the method by using it for a song about boredom and Benjamin Britten used a twelve tone row a tema seriale con fuga in his Cantata Academica Carmen Basiliense 1959 as an emblem of academicism 36 Schoenberg s mature practice editTen features of Schoenberg s mature twelve tone practice are characteristic interdependent and interactive 37 Hexachordal inversional combinatoriality Aggregates Linear set presentation Partitioning Isomorphic partitioning Invariants Hexachordal levels Harmony consistent with and derived from the properties of the referential set Metre established through pitch relational characteristics Multidimensional set presentations See also editList of dodecaphonic and serial compositions All interval twelve tone row All interval tetrachord All trichord hexachord Pitch interval List of tone rows and seriesReferences editNotes edit Whittall 2008 26 a b Perle 1991 145 a b Perle 1977 2 a b Schoenberg 1975 218 Whittall 2008 25 Leeuw 2005 149 Leeuw 2005 155 157 Schoenberg 1975 213 Perle 1977 9 10 a b Perle 1977 37 Neighbour 1955 53 John Covach quoted in Whittall 2008 24 a b c Whittall 2008 24 Reti 1958 Chase 1987 587 Yowp 7 January 2017 Tralfaz Cartoon Composer Scott Bradley Goldmark Daniel 2007 Tunes for Toons Music and the Hollywood Cartoon Univ of California Press p 71 ISBN 978 0 520 25311 7 Scott Bradley at IMDb Mustein Dave 2 November 2011 Blotted Science s Ron Jarzombek The Twelve tone Metalsucks Interview MetalSucks Retrieved 19 January 2021 Perle 1977 3 Whittall 2008 52 Bailey Kathryn 2006 The twelve note music of Anton Webern old forms in a new language Music in the twentieth century Digitally printed 1st pbk version ed Cambridge England New York Cambridge University Press p 31 ISBN 978 0 521 39088 0 Bailey Kathryn 2006 The twelve note music of Anton Webern old forms in a new language Music in the twentieth century Digitally printed 1st pbk version ed Cambridge England New York Cambridge University Press p 449 ISBN 978 0 521 39088 0 Moseley Brian 1 September 2019 Transformation Chains Associative Areas and a Principle of Form for Anton Webern s Twelve tone Music Music Theory Spectrum 41 2 218 243 doi 10 1093 mts mtz010 ISSN 0195 6167 Moseley Brian 2018 Cycles in Webern s Late Music Journal of Music Theory 62 2 165 204 doi 10 1215 00222909 7127658 ISSN 0022 2909 S2CID 171497028 Loy 2007 310 Benson 2007 348 Haimo 1990 27 Perle 1977 91 93 Babbitt 1960 249 250 Haimo 1990 13 Alegant 2010 20 a b Alegant 2010 21 Alegant 2010 22 24 Spies 1965 118 Brett 2007 Haimo 1990 41 Sources edit Alegant Brian 2010 The Twelve Tone Music of Luigi Dallapiccola Eastman Studies in Music 76 Rochester New York University of Rochester Press ISBN 978 1 58046 325 6 Babbitt Milton 1960 Twelve Tone Invariants as Compositional Determinants The Musical Quarterly 46 no 2 Special Issue Problems of Modern Music The Princeton Seminar in Advanced Musical Studies April 246 259 doi 10 1093 mq XLVI 2 246 JSTOR 740374 subscription required Babbitt Milton 1961 Set Structure as a Compositional Determinant Journal of Music Theory 5 no 1 Spring 72 94 JSTOR 842871 subscription required Benson Dave 2007 Music A Mathematical Offering Cambridge and New York Cambridge University Press ISBN 978 0 521 85387 3 Brett Philip Britten Benjamin Grove Music Online ed L Macy Accessed 8 January 2007 Chase Gilbert 1987 America s Music From the Pilgrims to the Present revised third edition Music in American Life Urbana University of Illinois Press ISBN 0 252 00454 X cloth ISBN 0 252 06275 2 pbk Haimo Ethan 1990 Schoenberg s Serial Odyssey The Evolution of his Twelve Tone Method 1914 1928 Oxford England Clarendon Press New York Oxford University Press ISBN 0 19 315260 6 Hill Richard S 1936 Schoenberg s Tone Rows and the Tonal System of the Future The Musical Quarterly 22 no 1 January 14 37 doi 10 1093 mq XXII 1 14 JSTOR 739013 subscription required Lansky Paul George Perle and Dave Headlam 2001 Twelve note Composition The New Grove Dictionary of Music and Musicians second edition edited by Stanley Sadie and John Tyrrell London Macmillan Leeuw Ton de 2005 Music of the Twentieth Century A Study of Its Elements and Structure translated from the Dutch by Stephen Taylor Amsterdam Amsterdam University Press ISBN 90 5356 765 8 Translation of Muziek van de twintigste eeuw een onderzoek naar haar elementen en structuur Utrecht Oosthoek 1964 Third impression Utrecht Bohn Scheltema amp Holkema 1977 ISBN 90 313 0244 9 Loy D Gareth 2007 Musimathics The Mathematical Foundations of Music Vol 1 Cambridge Massachusetts and London MIT Press ISBN 978 0 262 12282 5 Neighbour Oliver 1954 The Evolution of Twelve Note Music Proceedings of the Royal Musical Association volume 81 issue 1 49 61 doi 10 1093 jrma 81 1 49 Perle George 1977 Serial Composition and Atonality An Introduction to the Music of Schoenberg Berg and Webern fourth edition revised Berkeley Los Angeles and London University of California Press ISBN 0 520 03395 7 Perle George 1991 Serial Composition and Atonality An Introduction to the Music of Schoenberg Berg and Webern sixth edition revised Berkeley University of California Press ISBN 978 0 520 07430 9 Reti Rudolph 1958 Tonality Atonality Pantonality A Study of Some Trends in Twentieth Century Music Westport Connecticut Greenwood Press ISBN 0 313 20478 0 Rufer Josef 1954 Composition with Twelve Notes Related Only to One Another translated by Humphrey Searle New York The Macmillan Company Original German ed 1952 Schoenberg Arnold 1975 Style and Idea edited by Leonard Stein with translations by Leo Black Berkeley amp Los Angeles University of California Press ISBN 0 520 05294 3 207 208 Twelve Tone Composition 1923 214 245 Composition with Twelve Tones 1 1941 245 249 Composition with Twelve Tones 2 c 1948 Solomon Larry 1973 New Symmetric Transformations Perspectives of New Music 11 no 2 Spring Summer 257 264 JSTOR 832323 subscription required Spies Claudio 1965 Notes on Stravinsky s Abraham and Isaac Perspectives of New Music 3 no 2 Spring Summer 104 126 JSTOR 832508 subscription required Whittall Arnold 2008 The Cambridge Introduction to Serialism Cambridge Introductions to Music New York Cambridge University Press ISBN 978 0 521 86341 4 cloth ISBN 978 0 521 68200 8 pbk Further reading edit Covach John 1992 The Zwolftonspiel of Josef Matthias Hauer Journal of Music Theory 36 no 1 Spring 149 84 JSTOR 843913 subscription required Covach John 2000 Schoenberg s Poetics of Music the Twelve tone Method and the Musical Idea In Schoenberg and Words The Modernist Years edited by Russell A Berman and Charlotte M Cross New York Garland ISBN 0 8153 2830 3 Covach John 2002 Twelve tone Theory In The Cambridge History of Western Music Theory edited by Thomas Christensen 603 627 Cambridge Cambridge University Press ISBN 0 521 62371 5 Krenek Ernst 1953 Is the Twelve Tone Technique on the Decline The Musical Quarterly 39 no 4 October 513 527 Sedivy Dominik 2011 Serial Composition and Tonality An Introduction to the Music of Hauer and Steinbauer edited by Gunther Friesinger Helmut Neumann and Dominik Sedivy Vienna edition mono ISBN 3 902796 03 0 Sloan Susan L 1989 Archival Exhibit Schoenberg s Dodecaphonic Devices Journal of the Arnold Schoenberg Institute 12 no 2 November 202 205 Starr Daniel 1978 Sets Invariance and Partitions Journal of Music Theory 22 no 1 Spring 1 42 JSTOR 843626 subscription required Wuorinen Charles 1979 Simple Composition New York Longman ISBN 0 582 28059 1 Reprinted 1991 New York C F Peters ISBN 0 938856 06 5 External links edit nbsp Wikimedia Commons has media related to Twelve tone technique nbsp Wikiquote has quotations related to Twelve tone technique Twelve tone square to find all combinations of a 12 tone sequence New Transformations Beyond P I R and RI by Larry Solomon Javascript twelve tone matrix calculator and tone row analyzer Matrix generator from musictheory net by Ricci Adams Twelve Tone Technique A Quick Reference by Dan Roman Twelve Tones by mathemusician Vi Hart on YouTube Dodecaphonic Knots and Topology of Words by Franck Jedrzejewski fr Database on tone rows and tropes Portal nbsp Classical music Retrieved from https en wikipedia org w index php title Twelve tone technique amp oldid 1192116684, wikipedia, wiki, book, books, library,

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